DthetaphiTra: Mid/spr distance between trapezoidal fuzzy numbers
In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function calculates the mid/spr distance between the trapezoidal fuzzy numbers contained in two matrixes, which should be given in the desired format. For this, the function first checks if the input matrixes R and S are in the correct form (tested by checkingTra).

1	DthetaphiTra(R, S, a = 1, b = 1, theta = 1/3)

`R`	matrix of dimension `r x 4` containing `r` trapezoidal fuzzy numbers characterized by their four values `inf0,inf1,sup1,sup0`. The function first calls `checkingTra` to check if the matrix `R` has the correct format.
`S`	matrix of dimension `s x 4` containing `s` trapezoidal fuzzy numbers characterized by their four values `inf0,inf1,sup1,sup0`. The function first calls `checkingTra` to check if the matrix `S` has the correct format.
`a`	number >0, by default `a`=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1].
`b`	number >0, by default `b`=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1].
`theta`	number >0, by default `theta`=1/3. It is the weight of the spread in the mid/spr distance.

See examples

The function returns a matrix of dimension r x s containing the mid/spr distances between the trapezoidal fuzzy numbers of the matrix R and the trapezoidal fuzzy numbers of the matrix S.

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

[1] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, pp. 918-929 (2016)

checkingTra, Dthetaphi

# Example 1:
F=SimulCASE1(6)
S=SimulCASE1(8)
DthetaphiTra(F,S)

# Example 2:
F=matrix(c(1,1,0,2,3,4,5,6),nrow=2)
S=SimulCASE1(8)
DthetaphiTra(F,S,1,1,1)